Indeed, it has recently been established that stationary black hole geometries are endowed with horizon symmetries, classified as supertranslations and superrotations [1]}, [2]} (see [3]}, [4]}, [5]}, [6]} for older work on this topic).
Generic fluid flows which possess enstrophy are not stationary and imply non stationary dual black hole configurations. While the definition of supertranslations and superrotations may be extended to non stationary black holes, they are generally not associated with conserved currents [7]}.
